The president's move to placate millions of Americans on Thursday rattled health insurers, who said they were unsure how to revive canceled policies in short order.

While companies had expected the White House to address the white-hot issue of policy cancellations, President Barack Obama's decision to let people keep their old policies undercuts years of preparations for the overhaul of the health-insurance market and introduces new uncertainties. Two senior insurance executives said they had not yet received any formal...